diff --git a/CHANGELOG.md b/CHANGELOG.md
index 18e90ff9..ddbae8e9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - Add context.h functions (`PyContext_New`, etc) to FFI. [#1259](https://github.com/PyO3/pyo3/pull/1259)
 - Add `PyAny::is_instance()` method. [#1276](https://github.com/PyO3/pyo3/pull/1276)
 - Add support for conversion between `char` and `PyString`. [#1282](https://github.com/PyO3/pyo3/pull/1282)
+- Add FFI definitions for `PyBuffer_SizeFromFormat`, `PyObject_LengthHint`, `PyObject_CallNoArgs`, `PyObject_CallOneArg`, `PyObject_CallMethodNoArgs`, `PyObject_CallMethodOneArg`, `PyObject_VectorcallDict`, and `PyObject_VectorcallMethod`. [#1287](https://github.com/PyO3/pyo3/pull/1287)
 
 ### Changed
 - Change return type `PyType::name()` from `Cow<str>` to `PyResult<&str>`. [#1152](https://github.com/PyO3/pyo3/pull/1152)
@@ -29,6 +30,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - Change `Debug` and `Display` impls for `PyException` to be consistent with `PyAny`. [#1275](https://github.com/PyO3/pyo3/pull/1275)
 - Change `Debug` impl of `PyErr` to output more helpful information (acquiring the GIL if necessary). [#1275](https://github.com/PyO3/pyo3/pull/1275)
 - Rename `PyTypeInfo::is_instance` and `PyTypeInfo::is_exact_instance` to `PyTypeInfo::is_type_of` and `PyTypeInfo::is_exact_type_of`. [#1278](https://github.com/PyO3/pyo3/pull/1278)
+- Optimize `PyAny::call0`, `Py::call0` and `PyAny::call_method0` and `Py::call_method0` on Python 3.9 and up. [#1287](https://github.com/PyO3/pyo3/pull/1285)
 - Deprecate `Python::is_instance`, `Python::is_subclass`, `Python::release`, and `Python::xdecref`. [#1292](https://github.com/PyO3/pyo3/pull/1292)
 
 ### Removed
@@ -39,6 +41,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - Fix missing field in `PyCodeObject` struct (`co_posonlyargcount`) - caused invalid access to other fields in Python >3.7. [#1260](https://github.com/PyO3/pyo3/pull/1260)
 - Fix building for `x86_64-unknown-linux-musl` target from `x86_65-unknown-linux-gnu` host. [#1267](https://github.com/PyO3/pyo3/pull/1267)
 - Fix `#[text_signature]` interacting badly with rust `r#raw_identifiers`. [#1286](https://github.com/PyO3/pyo3/pull/1286)
+- Fix FFI definitions for `PyObject_Vectorcall` and `PyVectorcall_Call`. [#1287](https://github.com/PyO3/pyo3/pull/1285)
 - Fix building with Anaconda python inside a virtualenv. [#1290](https://github.com/PyO3/pyo3/pull/1290)
 
 ## [0.12.3] - 2020-10-12
diff --git a/Cargo.toml b/Cargo.toml
index 29a26741..9850271f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -15,6 +15,7 @@ build = "build.rs"
 edition = "2018"
 
 [dependencies]
+cfg-if = { version = "1.0" }
 ctor = { version = "0.1", optional = true }
 indoc = { version = "1.0.3", optional = true }
 inventory = { version = "0.1.4", optional = true }
diff --git a/benches/bench_call.rs b/benches/bench_call.rs
new file mode 100644
index 00000000..45b4ffd3
--- /dev/null
+++ b/benches/bench_call.rs
@@ -0,0 +1,53 @@
+#![feature(test)]
+
+extern crate test;
+use pyo3::prelude::*;
+use test::Bencher;
+
+macro_rules! test_module {
+    ($py:ident, $code:literal) => {
+        PyModule::from_code($py, indoc::indoc!($code), file!(), "test_module")
+            .expect("module creation failed")
+    };
+}
+
+#[bench]
+fn bench_call_0(b: &mut Bencher) {
+    Python::with_gil(|py| {
+        let module = test_module!(
+            py,
+            r#"
+            def foo(): pass
+        "#
+        );
+
+        let foo = module.getattr("foo").unwrap();
+
+        b.iter(|| {
+            for _ in 0..1000 {
+                foo.call0().unwrap();
+            }
+        });
+    })
+}
+
+#[bench]
+fn bench_call_method_0(b: &mut Bencher) {
+    Python::with_gil(|py| {
+        let module = test_module!(
+            py,
+            r#"
+            class Foo:
+                def foo(self): pass
+        "#
+        );
+
+        let foo = module.getattr("Foo").unwrap().call0().unwrap();
+
+        b.iter(|| {
+            for _ in 0..1000 {
+                foo.call_method0("foo").unwrap();
+            }
+        });
+    })
+}
diff --git a/src/ffi/cpython/abstract_.rs b/src/ffi/cpython/abstract_.rs
new file mode 100644
index 00000000..a2246708
--- /dev/null
+++ b/src/ffi/cpython/abstract_.rs
@@ -0,0 +1,306 @@
+use crate::ffi::{PyObject, Py_TYPE, Py_buffer, Py_ssize_t};
+use libc::{c_char, c_int, c_void};
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+use crate::ffi::{
+    vectorcallfunc, PyCallable_Check, PyThreadState, PyThreadState_GET, PyTuple_Check,
+    PyType_HasFeature, Py_TPFLAGS_HAVE_VECTORCALL,
+};
+#[cfg(all(Py_3_8, not(PyPy)))]
+use libc::size_t;
+
+extern "C" {
+    #[cfg(all(Py_3_8, not(PyPy)))]
+    pub fn _PyStack_AsDict(values: *const *mut PyObject, kwnames: *mut PyObject) -> *mut PyObject;
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+const _PY_FASTCALL_SMALL_STACK: size_t = 5;
+
+extern "C" {
+    #[cfg(all(Py_3_8, not(PyPy)))]
+    pub fn _Py_CheckFunctionResult(
+        tstate: *mut PyThreadState,
+        callable: *mut PyObject,
+        result: *mut PyObject,
+        where_: *const c_char,
+    ) -> *mut PyObject;
+
+    #[cfg(all(Py_3_8, not(PyPy)))]
+    pub fn _PyObject_MakeTpCall(
+        tstate: *mut PyThreadState,
+        callable: *mut PyObject,
+        args: *const *mut PyObject,
+        nargs: Py_ssize_t,
+        keywords: *mut PyObject,
+    ) -> *mut PyObject;
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+const PY_VECTORCALL_ARGUMENTS_OFFSET: Py_ssize_t =
+    1 << (8 * std::mem::size_of::<Py_ssize_t>() as Py_ssize_t - 1);
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyVectorcall_NARGS(n: size_t) -> Py_ssize_t {
+    assert!(n <= (Py_ssize_t::MAX as size_t));
+    (n as Py_ssize_t) & !PY_VECTORCALL_ARGUMENTS_OFFSET
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyVectorcall_Function(callable: *mut PyObject) -> Option<vectorcallfunc> {
+    assert!(!callable.is_null());
+    let tp = Py_TYPE(callable);
+    if PyType_HasFeature(tp, Py_TPFLAGS_HAVE_VECTORCALL) == 0 {
+        return None;
+    }
+    assert!(PyCallable_Check(callable) > 0);
+    let offset = (*tp).tp_vectorcall_offset;
+    assert!(offset > 0);
+    let ptr = (callable as *const c_char).offset(offset) as *const Option<vectorcallfunc>;
+    *ptr
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn _PyObject_VectorcallTstate(
+    tstate: *mut PyThreadState,
+    callable: *mut PyObject,
+    args: *const *mut PyObject,
+    nargsf: size_t,
+    kwnames: *mut PyObject,
+) -> *mut PyObject {
+    assert!(kwnames.is_null() || PyTuple_Check(kwnames) > 0);
+    assert!(!args.is_null() || PyVectorcall_NARGS(nargsf) == 0);
+
+    match PyVectorcall_Function(callable) {
+        None => {
+            let nargs = PyVectorcall_NARGS(nargsf);
+            _PyObject_MakeTpCall(tstate, callable, args, nargs, kwnames)
+        }
+        Some(func) => {
+            let res = func(callable, args, nargsf, kwnames);
+            _Py_CheckFunctionResult(tstate, callable, res, std::ptr::null_mut())
+        }
+    }
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyObject_Vectorcall(
+    callable: *mut PyObject,
+    args: *const *mut PyObject,
+    nargsf: size_t,
+    kwnames: *mut PyObject,
+) -> *mut PyObject {
+    _PyObject_VectorcallTstate(PyThreadState_GET(), callable, args, nargsf, kwnames)
+}
+
+extern "C" {
+    #[cfg(all(Py_3_8, not(PyPy)))]
+    #[cfg_attr(not(Py_3_9), link_name = "_PyObject_VectorcallDict")]
+    pub fn PyObject_VectorcallDict(
+        callable: *mut PyObject,
+        args: *const *mut PyObject,
+        nargsf: size_t,
+        kwargs: *mut PyObject,
+    ) -> *mut PyObject;
+
+    #[cfg(all(Py_3_8, not(PyPy)))]
+    #[cfg_attr(not(Py_3_9), link_name = "_PyVectorcall_Call")]
+    pub fn PyVectorcall_Call(
+        callable: *mut PyObject,
+        tuple: *mut PyObject,
+        dict: *mut PyObject,
+    ) -> *mut PyObject;
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn _PyObject_FastCallTstate(
+    tstate: *mut PyThreadState,
+    func: *mut PyObject,
+    args: *const *mut PyObject,
+    nargs: Py_ssize_t,
+) -> *mut PyObject {
+    _PyObject_VectorcallTstate(tstate, func, args, nargs as size_t, std::ptr::null_mut())
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn _PyObject_FastCall(
+    func: *mut PyObject,
+    args: *const *mut PyObject,
+    nargs: Py_ssize_t,
+) -> *mut PyObject {
+    _PyObject_FastCallTstate(PyThreadState_GET(), func, args, nargs)
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn _PyObject_CallNoArg(func: *mut PyObject) -> *mut PyObject {
+    _PyObject_VectorcallTstate(
+        PyThreadState_GET(),
+        func,
+        std::ptr::null_mut(),
+        0,
+        std::ptr::null_mut(),
+    )
+}
+
+#[cfg(all(Py_3_8, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyObject_CallOneArg(func: *mut PyObject, arg: *mut PyObject) -> *mut PyObject {
+    assert!(!arg.is_null());
+    let _args = [std::ptr::null_mut(), arg];
+    let args = _args.as_ptr().offset(1); // For PY_VECTORCALL_ARGUMENTS_OFFSET
+    let tstate = PyThreadState_GET();
+    let nargsf = 1 | PY_VECTORCALL_ARGUMENTS_OFFSET;
+    _PyObject_VectorcallTstate(tstate, func, args, nargsf as size_t, std::ptr::null_mut())
+}
+
+extern "C" {
+    #[cfg(all(Py_3_9, not(PyPy)))]
+    pub fn PyObject_VectorcallMethod(
+        name: *mut PyObject,
+        args: *const *mut PyObject,
+        nargsf: size_t,
+        kwnames: *mut PyObject,
+    ) -> *mut PyObject;
+}
+
+#[cfg(all(Py_3_9, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyObject_CallMethodNoArgs(
+    self_: *mut PyObject,
+    name: *mut PyObject,
+) -> *mut PyObject {
+    PyObject_VectorcallMethod(
+        name,
+        &self_,
+        1 | PY_VECTORCALL_ARGUMENTS_OFFSET as size_t,
+        std::ptr::null_mut(),
+    )
+}
+
+#[cfg(all(Py_3_9, not(PyPy)))]
+#[inline(always)]
+pub unsafe fn PyObject_CallMethodOneArg(
+    self_: *mut PyObject,
+    name: *mut PyObject,
+    arg: *mut PyObject,
+) -> *mut PyObject {
+    let args = [self_, arg];
+    assert!(!arg.is_null());
+    PyObject_VectorcallMethod(
+        name,
+        args.as_ptr(),
+        2 | PY_VECTORCALL_ARGUMENTS_OFFSET as size_t,
+        std::ptr::null_mut(),
+    )
+}
+
+// skipped _PyObject_VectorcallMethodId
+// skipped _PyObject_CallMethodIdNoArgs
+// skipped _PyObject_CallMethodIdOneArg
+
+// skipped _PyObject_HasLen
+
+extern "C" {
+    #[cfg_attr(PyPy, link_name = "PyPyObject_LengthHint")]
+    pub fn PyObject_LengthHint(o: *mut PyObject, arg1: Py_ssize_t) -> Py_ssize_t;
+
+    #[cfg(all(Py_3_9, not(PyPy)))]
+    pub fn PyObject_CheckBuffer(obj: *mut PyObject) -> c_int;
+}
+
+#[cfg(not(any(Py_3_9, PyPy)))]
+#[inline]
+pub unsafe fn PyObject_CheckBuffer(o: *mut PyObject) -> c_int {
+    let tp_as_buffer = (*Py_TYPE(o)).tp_as_buffer;
+    (!tp_as_buffer.is_null() && (*tp_as_buffer).bf_getbuffer.is_some()) as c_int
+}
+
+extern "C" {
+    #[cfg_attr(PyPy, link_name = "PyPyObject_GetBuffer")]
+    pub fn PyObject_GetBuffer(obj: *mut PyObject, view: *mut Py_buffer, flags: c_int) -> c_int;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_GetPointer")]
+    pub fn PyBuffer_GetPointer(view: *mut Py_buffer, indices: *mut Py_ssize_t) -> *mut c_void;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_SizeFromFormat")]
+    pub fn PyBuffer_SizeFromFormat(format: *const c_char) -> Py_ssize_t;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_ToContiguous")]
+    pub fn PyBuffer_ToContiguous(
+        buf: *mut c_void,
+        view: *mut Py_buffer,
+        len: Py_ssize_t,
+        order: c_char,
+    ) -> c_int;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_FromContiguous")]
+    pub fn PyBuffer_FromContiguous(
+        view: *mut Py_buffer,
+        buf: *mut c_void,
+        len: Py_ssize_t,
+        order: c_char,
+    ) -> c_int;
+    pub fn PyObject_CopyData(dest: *mut PyObject, src: *mut PyObject) -> c_int;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_IsContiguous")]
+    pub fn PyBuffer_IsContiguous(view: *const Py_buffer, fort: c_char) -> c_int;
+    pub fn PyBuffer_FillContiguousStrides(
+        ndims: c_int,
+        shape: *mut Py_ssize_t,
+        strides: *mut Py_ssize_t,
+        itemsize: c_int,
+        fort: c_char,
+    );
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_FillInfo")]
+    pub fn PyBuffer_FillInfo(
+        view: *mut Py_buffer,
+        o: *mut PyObject,
+        buf: *mut c_void,
+        len: Py_ssize_t,
+        readonly: c_int,
+        flags: c_int,
+    ) -> c_int;
+    #[cfg_attr(PyPy, link_name = "PyPyBuffer_Release")]
+    pub fn PyBuffer_Release(view: *mut Py_buffer);
+}
+
+#[inline]
+pub unsafe fn PyIter_Check(o: *mut PyObject) -> c_int {
+    (match (*Py_TYPE(o)).tp_iternext {
+        Some(tp_iternext) => {
+            tp_iternext as *const c_void != crate::ffi::object::_PyObject_NextNotImplemented as _
+        }
+        None => false,
+    }) as c_int
+}
+
+// skipped PySequence_ITEM
+
+pub const PY_ITERSEARCH_COUNT: c_int = 1;
+pub const PY_ITERSEARCH_INDEX: c_int = 2;
+pub const PY_ITERSEARCH_CONTAINS: c_int = 3;
+
+extern "C" {
+    #[cfg(not(PyPy))]
+    pub fn _PySequence_IterSearch(
+        seq: *mut PyObject,
+        obj: *mut PyObject,
+        operation: c_int,
+    ) -> Py_ssize_t;
+}
+
+// skipped _PyObject_RealIsInstance
+// skipped _PyObject_RealIsSubclass
+
+// skipped _PySequence_BytesToCharpArray
+
+// skipped _Py_FreeCharPArray
+
+// skipped _Py_add_one_to_index_F
+// skipped _Py_add_one_to_index_C
+
+// skipped _Py_convert_optional_to_ssize_t
+
+// skipped _PyNumber_Index(*mut PyObject o)
diff --git a/src/ffi/cpython/mod.rs b/src/ffi/cpython/mod.rs
new file mode 100644
index 00000000..7164f260
--- /dev/null
+++ b/src/ffi/cpython/mod.rs
@@ -0,0 +1,3 @@
+pub mod abstract_;
+
+pub use self::abstract_::*;
diff --git a/src/ffi/methodobject.rs b/src/ffi/methodobject.rs
index 193dde8b..91dd2d6f 100644
--- a/src/ffi/methodobject.rs
+++ b/src/ffi/methodobject.rs
@@ -16,40 +16,6 @@ pub unsafe fn PyCFunction_Check(op: *mut PyObject) -> c_int {
 pub type PyCFunction =
     unsafe extern "C" fn(slf: *mut PyObject, args: *mut PyObject) -> *mut PyObject;
 
-// TODO(davidhewitt)[1283] - Fix this definition
-// #[cfg(all(Py_3_8, not(Py_LIMITED_API)))]
-// #[cfg_attr(Py_3_8, link_name = "_PyObject_Vectorcall")]
-// pub type PyObject_Vectorcall = unsafe extern "C" fn(
-//     slf: *mut PyObject,
-//     // positional and keyword arguments
-//     args: *const *mut PyObject,
-//     // number of position arguments in args, after which values are kwargs
-//     nargs: crate::ffi::pyport::Py_ssize_t,
-//     // tuple of kwargs, if given, or null
-//     kwnames: *mut PyObject,
-// ) -> *mut PyObject;
-
-// TODO(davidhewitt)[1283] - Fix this definition
-// #[cfg(all(Py_3_8, not(Py_LIMITED_API)))]
-// #[cfg_attr(Py_3_8, link_name = "PyVectorcall_Call")]
-// pub type PyVectorcall_Call = unsafe extern "C" fn(
-//     obj: *mut PyObject,
-//     tuple: *mut PyObject,
-//     dict: *mut PyObject,
-// ) -> *mut PyObject;
-
-#[cfg(all(Py_3_7, not(Py_LIMITED_API)))]
-const PY_VECTORCALL_ARGUMENTS_OFFSET: crate::ffi::pyport::Py_ssize_t =
-    1 << (8 * std::mem::size_of::<usize>() - 1);
-
-#[cfg(all(Py_3_7, not(Py_LIMITED_API)))]
-#[inline(always)]
-pub unsafe fn PyVectorcall_NARGS(
-    n: crate::ffi::pyport::Py_ssize_t,
-) -> crate::ffi::pyport::Py_ssize_t {
-    n & !PY_VECTORCALL_ARGUMENTS_OFFSET
-}
-
 #[cfg(all(Py_3_7, not(Py_LIMITED_API)))]
 pub type _PyCFunctionFast = unsafe extern "C" fn(
     slf: *mut PyObject,
diff --git a/src/ffi/mod.rs b/src/ffi/mod.rs
index cd901103..2edb2768 100644
--- a/src/ffi/mod.rs
+++ b/src/ffi/mod.rs
@@ -61,6 +61,9 @@ pub use self::unicodeobject::*;
 pub use self::warnings::*;
 pub use self::weakrefobject::*;
 
+#[cfg(not(Py_LIMITED_API))]
+pub use self::cpython::*;
+
 mod pyport;
 // mod pymacro; contains nothing of interest for Rust
 // mod pyatomic; contains nothing of interest for Rust
@@ -169,3 +172,6 @@ pub(crate) mod datetime;
 pub(crate) mod marshal;
 
 pub(crate) mod funcobject;
+
+#[cfg(not(Py_LIMITED_API))]
+mod cpython;
diff --git a/src/ffi/object.rs b/src/ffi/object.rs
index 10255639..99fc3798 100644
--- a/src/ffi/object.rs
+++ b/src/ffi/object.rs
@@ -758,7 +758,7 @@ pub const Py_TPFLAGS_BASETYPE: c_ulong = 1 << 10;
 
 /// Set if the type implements the vectorcall protocol (PEP 590)
 #[cfg(all(Py_3_8, not(Py_LIMITED_API)))]
-pub const _Py_TPFLAGS_HAVE_VECTORCALL: c_ulong = 1 << 11;
+pub const Py_TPFLAGS_HAVE_VECTORCALL: c_ulong = 1 << 11;
 
 /// Set if the type is 'ready' -- fully initialized
 pub const Py_TPFLAGS_READY: c_ulong = 1 << 12;
diff --git a/src/ffi/objectabstract.rs b/src/ffi/objectabstract.rs
index bead5ebf..07116e4e 100644
--- a/src/ffi/objectabstract.rs
+++ b/src/ffi/objectabstract.rs
@@ -1,6 +1,6 @@
 use crate::ffi::object::*;
 use crate::ffi::pyport::Py_ssize_t;
-use std::os::raw::{c_char, c_int, c_void};
+use std::os::raw::{c_char, c_int};
 use std::ptr;
 
 #[inline]
@@ -16,6 +16,11 @@ pub unsafe fn PyObject_DelAttr(o: *mut PyObject, attr_name: *mut PyObject) -> c_
 }
 
 extern "C" {
+    #[cfg(all(
+        not(PyPy),
+        any(not(Py_LIMITED_API), Py_3_9) // Added to limited API in 3.9
+    ))]
+    pub fn PyObject_CallNoArgs(func: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyObject_Call")]
     pub fn PyObject_Call(
         callable_object: *mut PyObject,
@@ -61,10 +66,6 @@ pub unsafe fn PyObject_Length(o: *mut PyObject) -> Py_ssize_t {
 }
 
 extern "C" {
-    #[cfg(not(Py_LIMITED_API))]
-    #[cfg_attr(PyPy, link_name = "PyPyObject_LengthHint")]
-    pub fn PyObject_LengthHint(o: *mut PyObject, arg1: Py_ssize_t) -> Py_ssize_t;
-
     #[cfg_attr(PyPy, link_name = "PyPyObject_GetItem")]
     pub fn PyObject_GetItem(o: *mut PyObject, key: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyObject_SetItem")]
@@ -73,78 +74,15 @@ extern "C" {
     pub fn PyObject_DelItem(o: *mut PyObject, key: *mut PyObject) -> c_int;
 }
 
-#[cfg(not(Py_LIMITED_API))]
-#[inline]
-pub unsafe fn PyObject_CheckBuffer(o: *mut PyObject) -> c_int {
-    let tp_as_buffer = (*Py_TYPE(o)).tp_as_buffer;
-    (!tp_as_buffer.is_null() && (*tp_as_buffer).bf_getbuffer.is_some()) as c_int
-}
-
-#[cfg(not(Py_LIMITED_API))]
-extern "C" {
-    #[cfg_attr(PyPy, link_name = "PyPyObject_GetBuffer")]
-    pub fn PyObject_GetBuffer(obj: *mut PyObject, view: *mut Py_buffer, flags: c_int) -> c_int;
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_GetPointer")]
-    pub fn PyBuffer_GetPointer(view: *mut Py_buffer, indices: *mut Py_ssize_t) -> *mut c_void;
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_ToContiguous")]
-    pub fn PyBuffer_ToContiguous(
-        buf: *mut c_void,
-        view: *mut Py_buffer,
-        len: Py_ssize_t,
-        order: c_char,
-    ) -> c_int;
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_FromContiguous")]
-    pub fn PyBuffer_FromContiguous(
-        view: *mut Py_buffer,
-        buf: *mut c_void,
-        len: Py_ssize_t,
-        order: c_char,
-    ) -> c_int;
-    pub fn PyObject_CopyData(dest: *mut PyObject, src: *mut PyObject) -> c_int;
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_IsContiguous")]
-    pub fn PyBuffer_IsContiguous(view: *const Py_buffer, fort: c_char) -> c_int;
-    pub fn PyBuffer_FillContiguousStrides(
-        ndims: c_int,
-        shape: *mut Py_ssize_t,
-        strides: *mut Py_ssize_t,
-        itemsize: c_int,
-        fort: c_char,
-    );
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_FillInfo")]
-    pub fn PyBuffer_FillInfo(
-        view: *mut Py_buffer,
-        o: *mut PyObject,
-        buf: *mut c_void,
-        len: Py_ssize_t,
-        readonly: c_int,
-        flags: c_int,
-    ) -> c_int;
-    #[cfg_attr(PyPy, link_name = "PyPyBuffer_Release")]
-    pub fn PyBuffer_Release(view: *mut Py_buffer);
-}
-
 extern "C" {
     #[cfg_attr(PyPy, link_name = "PyPyObject_Format")]
     pub fn PyObject_Format(obj: *mut PyObject, format_spec: *mut PyObject) -> *mut PyObject;
     #[cfg_attr(PyPy, link_name = "PyPyObject_GetIter")]
     pub fn PyObject_GetIter(arg1: *mut PyObject) -> *mut PyObject;
-}
 
-#[cfg(not(Py_LIMITED_API))]
-#[inline]
-#[cfg_attr(PyPy, link_name = "PyPyIter_Check")]
-pub unsafe fn PyIter_Check(o: *mut PyObject) -> c_int {
-    (match (*Py_TYPE(o)).tp_iternext {
-        Some(tp_iternext) => {
-            tp_iternext as *const c_void
-                != crate::ffi::object::_PyObject_NextNotImplemented as *const c_void
-        }
-        None => false,
-    }) as c_int
-}
-
-#[cfg(all(Py_LIMITED_API, Py_3_8))]
-extern "C" {
+    // PyIter_Check for unlimited API is in cpython/abstract_.rs
+    #[cfg(all(Py_LIMITED_API, Py_3_8))]
+    #[cfg_attr(PyPy, link_name = "PyPyIter_Check")]
     pub fn PyIter_Check(obj: *mut PyObject) -> c_int;
 }
 
diff --git a/src/instance.rs b/src/instance.rs
index 9cfc4002..45d3a169 100644
--- a/src/instance.rs
+++ b/src/instance.rs
@@ -272,7 +272,18 @@ impl<T> Py<T> {
     ///
     /// This is equivalent to the Python expression `self()`.
     pub fn call0(&self, py: Python) -> PyResult<PyObject> {
-        self.call(py, (), None)
+        cfg_if::cfg_if! {
+            // TODO: Use PyObject_CallNoArgs instead after https://bugs.python.org/issue42415.
+            // Once the issue is resolved, we can enable this optimization for limited API.
+            if #[cfg(all(Py_3_9, not(Py_LIMITED_API)))] {
+                // Optimized path on python 3.9+
+                unsafe {
+                    PyObject::from_owned_ptr_or_err(py, ffi::_PyObject_CallNoArg(self.as_ptr()))
+                }
+            } else {
+                self.call(py, (), None)
+            }
+        }
     }
 
     /// Calls a method on the object.
@@ -316,7 +327,17 @@ impl<T> Py<T> {
     ///
     /// This is equivalent to the Python expression `self.name()`.
     pub fn call_method0(&self, py: Python, name: &str) -> PyResult<PyObject> {
-        self.call_method(py, name, (), None)
+        cfg_if::cfg_if! {
+            if #[cfg(all(Py_3_9, not(Py_LIMITED_API)))] {
+                // Optimized path on python 3.9+
+                unsafe {
+                    let name = name.into_py(py);
+                    PyObject::from_owned_ptr_or_err(py, ffi::PyObject_CallMethodNoArgs(self.as_ptr(), name.as_ptr()))
+                }
+            } else {
+                self.call_method(py, name, (), None)
+            }
+        }
     }
 
     /// Create a `Py<T>` instance by taking ownership of the given FFI pointer.
diff --git a/src/types/any.rs b/src/types/any.rs
index 1a79aa58..5e8c2ff1 100644
--- a/src/types/any.rs
+++ b/src/types/any.rs
@@ -226,7 +226,18 @@ impl PyAny {
     ///
     /// This is equivalent to the Python expression `self()`.
     pub fn call0(&self) -> PyResult<&PyAny> {
-        self.call((), None)
+        cfg_if::cfg_if! {
+            // TODO: Use PyObject_CallNoArgs instead after https://bugs.python.org/issue42415.
+            // Once the issue is resolved, we can enable this optimization for limited API.
+            if #[cfg(all(Py_3_9, not(Py_LIMITED_API)))] {
+                // Optimized path on python 3.9+
+                unsafe {
+                    self.py().from_owned_ptr_or_err(ffi::_PyObject_CallNoArg(self.as_ptr()))
+                }
+            } else {
+                self.call((), None)
+            }
+        }
     }
 
     /// Calls the object with only positional arguments.
@@ -283,7 +294,17 @@ impl PyAny {
     ///
     /// This is equivalent to the Python expression `self.name()`.
     pub fn call_method0(&self, name: &str) -> PyResult<&PyAny> {
-        self.call_method(name, (), None)
+        cfg_if::cfg_if! {
+            if #[cfg(all(Py_3_9, not(Py_LIMITED_API)))] {
+                // Optimized path on python 3.9+
+                unsafe {
+                    let name = name.into_py(self.py());
+            self.py().from_owned_ptr_or_err(ffi::PyObject_CallMethodNoArgs(self.as_ptr(), name.as_ptr()))
+                }
+            } else {
+                self.call_method(name, (), None)
+            }
+        }
     }
 
     /// Calls a method on the object with only positional arguments.
@@ -464,8 +485,17 @@ impl PyAny {
 
 #[cfg(test)]
 mod test {
-    use crate::types::{IntoPyDict, PyList, PyLong};
-    use crate::{Python, ToPyObject};
+    use crate::{
+        types::{IntoPyDict, PyList, PyLong, PyModule},
+        Python, ToPyObject,
+    };
+
+    macro_rules! test_module {
+        ($py:ident, $code:literal) => {
+            PyModule::from_code($py, indoc::indoc!($code), file!(), "test_module")
+                .expect("module creation failed")
+        };
+    }
 
     #[test]
     fn test_call_for_non_existing_method() {
@@ -488,6 +518,30 @@ mod test {
         assert_eq!(list.extract::<Vec<i32>>(py).unwrap(), vec![7, 6, 5, 4, 3]);
     }
 
+    #[test]
+    fn test_call_method0() {
+        Python::with_gil(|py| {
+            let module = test_module!(
+                py,
+                r#"
+                class SimpleClass:
+                    def foo(self):
+                        return 42
+            "#
+            );
+
+            let simple_class = module.getattr("SimpleClass").unwrap().call0().unwrap();
+            assert_eq!(
+                simple_class
+                    .call_method0("foo")
+                    .unwrap()
+                    .extract::<u32>()
+                    .unwrap(),
+                42
+            );
+        })
+    }
+
     #[test]
     fn test_type() {
         let gil = Python::acquire_gil();